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A coin of mass m is at rest on a book cover which is at an incline angle relative to horizontal at as shown in the figure. There is friction f between the coin and the surface of the book so that the coin does not slide down the cover of the book.

A coin of mass m is at rest on a book cover which is at an incline angle relative to horizontal at as shown in the figure. There is friction f between the coin and the surface of the book so that the coin does not slide down the cover of the book.

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A coin of mass \( m \) is at rest on a book cover which is at an incline angle \( \theta \) relative to horizontal, as shown in the figure. There is friction \( f \) between the coin and the surface of the book so that the coin does not slide down the cover of the book. **(A)** Draw a free body diagram for the coin on the surface of the inclined book cover, including all forces acting on the block as vectors. Make sure to label the vectors. Include x and y axes in your sketch (feel free to draw axes in any orientation you would like). **(B)** Use Newton's second law to write equations for forces acting on the coin in x and y dimensions (separately) as a function of the frictional force \( f \), the mass of the coin \( m \), the gravitational constant \( g \), and the angle of the incline \( \theta \). **(C)** If the coin has a mass of 5.0 grams and the coefficient of static friction \( \mu_s \) is 0.37, find the maximum angle \( \theta_{\text{max}} \) such that the coin is stationary (i.e., does not slide). --- The corresponding image shows: - A book partially open with its cover inclined and placed on a flat surface. - A hand is holding the book open. - A coin is placed on the inclined cover with an angle of 7° indicated. Use this setup to explain the concept of static friction and inclined planes in physics.
Transcribed Image Text:A coin of mass \( m \) is at rest on a book cover which is at an incline angle \( \theta \) relative to horizontal, as shown in the figure. There is friction \( f \) between the coin and the surface of the book so that the coin does not slide down the cover of the book. **(A)** Draw a free body diagram for the coin on the surface of the inclined book cover, including all forces acting on the block as vectors. Make sure to label the vectors. Include x and y axes in your sketch (feel free to draw axes in any orientation you would like). **(B)** Use Newton's second law to write equations for forces acting on the coin in x and y dimensions (separately) as a function of the frictional force \( f \), the mass of the coin \( m \), the gravitational constant \( g \), and the angle of the incline \( \theta \). **(C)** If the coin has a mass of 5.0 grams and the coefficient of static friction \( \mu_s \) is 0.37, find the maximum angle \( \theta_{\text{max}} \) such that the coin is stationary (i.e., does not slide). --- The corresponding image shows: - A book partially open with its cover inclined and placed on a flat surface. - A hand is holding the book open. - A coin is placed on the inclined cover with an angle of 7° indicated. Use this setup to explain the concept of static friction and inclined planes in physics.
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